Confining and chiral properties of QCD in extremely strong magnetic fields

Abstract

We investigate, by numerical lattice simulations, the static quark-antiquark potential, the flux tube properties and the chiral condensate for N f = 2 + 1 QCD with physical quark masses in the presence of strong magnetic fields, going up to eB = 9 GeV 2 , with continuum extrapolated results. The string tension for quark-antiquark separations longitudinal to the magnetic field is suppressed by one order of magnitude at the largest explored magnetic field with respect to its value at zero magnetic background, but is still non-vanishing; in the transverse direction, instead, the string tension is enhanced but seems to reach a saturation at around 50 % of its value at B = 0. The flux tube shows a consistent suppression/enhancement of the overall amplitude, with mild modifications of its profile. Finally, we observe magnetic catalysis in the whole range of explored fields with a behavior compatible with a lowest Landau level approximation, in particular with a linear dependence of the chiral condensate on B which is in agreement, within errors, with that already observed for eB ∼ 1 GeV 2 .

Quark condensate in QCD at nonzero magnetic field and temperature

“…In this way we obtain R th (4 GeV 2 ) = 4.39 and R th (9 GeV 2 ) = 11.56, while the lattice data from [14]) yield respectively (approximately from Fig 3 of [14]) R lat (4 GeV 2 ) = 4.8; R lat (9 GeV 2 ) = 12.6. One can see again a reasonable agreement, implying that our formalism, without any phase transitions, accurately describes the behavior at large eB.…”

“…which can be compared to numerous lattice data [4,5,6,7,8,9,10,11,12,13,14,15,16,17], e.g. in [30] Σ l = (283(2) MeV) 3 .…”

“…At this point it is important to study the general trend of the large eB chiral condensate, which according to [14] might show a possible sign of the of the vacuum transition connected to chiral magnetic effect. To this end we compare the ratio R lat (eB) = ∆Σu(eB)+∆Σ d (eB) ∆Σu(1 GeV 2 )+∆Σ d (1 GeV 2 ) from the lattice measurements in [16,14] with our calculations according to (23) where…”

“…Therefore the most important problem is to find the origin of this parameter and its connection and role in the overall dynamics of QCD, in particular, the connection of Σ i and the string tension σ, which provides confinement. This topic was intensively studied in the framework of the QCD lattice theory [4,5,6,7,8,9,10,11,12,13,14,15,16,17]. In the previous papers we have exploited the Chiral Confining theory (CCTh) [18,19,20,21,22,23] to calculate the chiral meson masses and the quark condensate via the string tension and the quark masses, where an additional parameter λ -the effective radius of the meson state, can be used as a multiplicative constant.…”

Phase diagram of QCD in a magnetic background

“…As in Refs. [18,23], we consider a discretization of N f = 2 + 1 QCD based on the tree-level improved Symanzik pure gauge action [24,25] and on stout rooted staggered fermions [26,27], i.e. on the following partition function…”